Searching Algorithms Questions Long
Exponential interpolation search is a searching algorithm that is used to find the position of a target value within a sorted array. It is an improved version of the binary search algorithm, which reduces the number of comparisons required to find the target value.
The time complexity of exponential interpolation search can be analyzed as follows:
1. Best-case time complexity:
In the best-case scenario, the target value is found at the first position itself. In this case, the time complexity of exponential interpolation search would be O(1), as only one comparison is required.
2. Average-case time complexity:
The average-case time complexity of exponential interpolation search is O(log(log(n))), where n is the size of the array. This is because the algorithm uses exponential interpolation to estimate the position of the target value. It starts by comparing the target value with the element at the first position, and if they match, the search is complete. Otherwise, it estimates the position of the target value using interpolation formula:
pos = low + ((target - arr[low]) * (high - low)) / (arr[high] - arr[low])
Here, "low" and "high" represent the current range of the array being searched. The algorithm then compares the target value with the element at the estimated position. If they match, the search is complete. Otherwise, it updates the range based on whether the target value is smaller or larger than the estimated element, and repeats the process until the target value is found or the range becomes empty.
The interpolation formula allows the algorithm to make a more informed guess about the position of the target value, resulting in fewer comparisons compared to binary search. However, the time complexity is still logarithmic due to the halving of the search range in each iteration.
3. Worst-case time complexity:
In the worst-case scenario, the target value is either the smallest or largest element in the array, or it is not present in the array at all. In this case, the time complexity of exponential interpolation search would be O(n), as the algorithm may need to compare the target value with all elements in the array before determining its absence.
It is important to note that the time complexity of exponential interpolation search assumes that the array is sorted. If the array is not sorted, the algorithm may not work correctly, and the time complexity would be different.
In conclusion, the time complexity of exponential interpolation search is O(log(log(n))) on average, O(1) in the best-case scenario, and O(n) in the worst-case scenario.